A fast statistical method for dispersion characteristics of acoustic logging while drilling

Abstract

The invention discloses a fast statistical method for dispersion characteristics of acoustic logging while drilling. Firstly, relevant parameters of acoustic logging while drilling are collected, and a dispersion equation is derived according to the collected parameters. Then, a dispersion model is constructed by solving the determinant of the dispersion equation. Then, the phase velocity and the attenuation coefficient are fixed respectively to perform matrix solution to find the local minimum value in the whole space, that is, the expected wave number to be solved. Finally, the dispersion characteristics are statistically analyzed according to the expected wave number, so that the geological structure and rock properties of the formation under the wellbore can be quickly and efficiently understood.

Description

Technical Field

[0001] The invention belongs to the technical field of logging while drilling, and more specifically, relates to a fast statistical method for frequency dispersion characteristics used for acoustic logging while drilling. Background Art

[0002] As drilling projects advance to deep and ultra-deep layers, the formation information obtained by radiating sound waves in the direction of the drill bit and inverting them is of great significance in improving drilling safety, geological guidance, oil and gas layer drilling rate and recovery rate. In forward-looking logging while drilling, the acoustic transducer is mainly installed on the drill collar, emitting sound waves into the wellbore and forming acoustic guided waves that propagate axially along the wellbore. When the axially propagating acoustic guided waves enter the bottom of the wellbore, a part of them is transmitted to the pre-drilling formation, thereby forming a forward-radiated acoustic wave for pre-drilling formation detection; when encountering obstacles in front, it is reflected back to the wellbore and received by the acoustic transducer, completing pre-drilling formation detection.

[0003] During the propagation of the acoustic wave, due to the existence of the wellbore, the acoustic wave transducer mounted on the wellbore measuring device transmits acoustic wave signals into the wellbore. The wave signals reflected and refracted in different media on the wellbore wall interfere with the original wave signals, generating wave signals of different frequencies, thus causing frequency dispersion.

[0004] Dispersion causes certain difficulties in echo analysis, so dispersion analysis is of great significance for understanding the propagation characteristics of each component wavelet. The acoustic field dispersion characteristics in LWD forward-looking logging mainly come from solving the dispersion equation. In order to obtain accurate dispersion characteristics, the logging instrument transmits sound waves to the well wall in real time and receives echoes, thereby obtaining the spacing between the drill collar and the well wall, substituting it into the dispersion equation to calculate the dispersion characteristics. However, due to the complexity of the equation, for many years, the first-order linear approximation method based on the Newton-Raphson method has been considered the standard method for solving the dispersion equation. However, if the variability of the cutoff frequency of different modal acoustic waves is taken into account, the dispersion curves of all modes may not be identified, and due to the internal iterative process, the calculation efficiency will be low. Therefore, in view of the challenges faced by adaptively solving the dispersion characteristics of the acoustic wave field in actual continuous logging operations, only by analyzing the dispersion characteristics of the acoustic wave field can we better understand the geological structure and rock properties of the formation below the wellbore, thereby providing a scientific basis for resource development and engineering construction. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a fast statistical method for the dispersion characteristics of acoustic logging while drilling, which can quickly obtain all real solutions of the dispersion equation and find local minima to effectively describe the dispersion characteristics of the wave field in the forward-looking logging while drilling.

[0006] To achieve the above-mentioned object of the invention, the present invention provides a fast statistical method for dispersion characteristics of acoustic logging while drilling, which is characterized by comprising the following steps:

[0007] (1) Data collection;

[0008] (1.1) Setting the frequency ω of the acoustic signal emitted by the borehole measurement device;

[0009] (1.2) Collect the density of drill collar, inner well fluid, outer well fluid and formation, record them as ρ1, ρ2, ρ3 and ρ4 respectively; measure the radius of drill collar r1, the radius of inner well fluid r2 and the radius of outer well fluid r3; measure the Young's modulus of drill collar and formation as E1 and E2 respectively and Poisson's ratio as ν1 and ν2 respectively;

[0010] (1.3) Calculate the borehole diameter r;

[0011] In the forward-looking acoustic logging while drilling, the borehole measurement device is set at an interval of 120°, and the acoustic pulse signal is transmitted in three directions respectively. The array receiver placed on the drill collar captures the echo signal, and then measures the time difference between the time of transmitting the acoustic signal and the time of receiving the reflected pulse signal. According to the acoustic wave velocity, the average borehole diameter r is calculated;

[0012] (2) Establish a dispersion model;

[0013] Based on the parameters collected in step (1), the dispersion equation D is derived using the global matrix method, and then the dispersion model G is set equal to the determinant of the dispersion equation D, thereby constructing the following dispersion model:

[0014]

[0015] in, represents the real wave number, represents the attenuation coefficient and satisfies: is the complex wave number, j represents the imaginary part; det[D] represents the determinant of the dispersion equation D;

[0016] (3) Dispersion analysis;

[0017] (3.1), transform the dispersion model G by taking its logarithm;

[0018]

[0019] (3.2), substitute the frequency ω of the acoustic wave signal into the logarithmic transformed dispersion model G, and then zrn , k zrm Sampling is performed separately to obtain (kz r n,1,kz r n,2,…,kz r n, N )、(kz r m,1,kz rm,2,…,kz r m, M ), where n = 1, 2, ..., N, m = 1, 2, ..., M, N and M represent the number of samples respectively;

[0020] (3.3), first fix k zrm The first point k in zrm,1 , and (k zrn,1 ,k zrn,2 ,…,k zrn,N ) are substituted into the logarithmically transformed dispersion model G to obtain N k zrn A matrix of points

[0021]

[0022] (3.4), in the matrix Fill the two ends of the matrix with 0 to get

[0023]

[0024] (3.5), from the matrix The difference operation starts from the second column, that is, each column is subtracted from the previous column elements to obtain the matrix

[0025] (3.6) By introducing the symbolic function The matrix The elements less than 0 are converted to 1, and the elements greater than 0 are converted to 0, resulting in the matrix

[0026] (3.7), from the matrix The difference operation starts from the second column, that is, each column is subtracted from the previous column elements to obtain the matrix Among them, the point corresponding to element -1 is the local minimum of the entire equation;

[0027] (3.8), fix the second point k zrm,2 To the Mth point k zrm,M , repeat steps (3.3) to (3.7) to obtain the first index matrix Mn(kz r n,kz r m);

[0028]

[0029] (3.9), fixed k zrn The first point k zrn,1 , put (k zrm,1 ,k zrm,2 ,…,k zrm,MSubstituting the values ​​in ) into the logarithmically transformed dispersion model G, we get M k zrm A matrix of points

[0030] (3.10) According to steps (3.3) to (3.8), we get the second index matrix Mm(kz r n,kz r m)

[0031]

[0032] (3.11), add the two index matrices together to get the total index matrix

[0033]

[0034] (3.12), find the total index matrix The point corresponding to the element value of -2 is the local minimum of the dispersion model G in the entire space, which is the expected wave number to be solved;

[0035] (4) Draw the dispersion characteristic curve;

[0036] The frequency ω of the acoustic wave signal emitted by the borehole measurement device is changed to obtain the expected wave number corresponding to different frequencies, and then the dispersion characteristic curve is drawn with different frequencies as the horizontal axis and the corresponding expected wave number as the vertical axis.

[0037] The object of the invention of the present invention is achieved in this way:

[0038] The invention discloses a fast statistical method for dispersion characteristics of acoustic logging while drilling. The method first collects relevant parameters of acoustic logging while drilling, and derives a dispersion equation according to the collected parameters. Then, a dispersion model is constructed by solving the determinant of the dispersion equation. Then, the phase velocity and the attenuation coefficient are fixed respectively to perform matrix solution to find the local minimum value in the entire space, that is, the expected wave number to be solved. Finally, the dispersion characteristics are statistically analyzed according to the expected wave number, so that the geological structure and rock properties of the formation below the wellbore can be quickly and efficiently understood. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flow chart of a fast statistical method for dispersion characteristics of acoustic logging while drilling;

[0040] Figure 2 It is a specific flow chart for solving the local minimum value of the dispersion model G using the fast statistical method of dispersion characteristics;

[0041] Figure 3 This is the visualization result of the dispersion model G after logarithmic transformation;

[0042] Figure 4 It is a visualization result diagram of the dispersion model G with the local minimum points marked; DETAILED DESCRIPTION

[0043] The specific implementation of the present invention is described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0044] Example

[0045] Figure 2 The present invention is a flow chart of a method for quickly calculating the dispersion characteristics of acoustic logging while drilling.

[0046] In this embodiment, a fast statistical method for dispersion characteristics of acoustic logging while drilling is invented, comprising the following steps:

[0047] S1, data collection;

[0048] S1.1. Set the frequency ω of the acoustic wave signal emitted by the borehole measurement device to 1kHz;

[0049] S1.2. Collect the density of drill collar, inner well fluid, outer well fluid and formation, record them as ρ1 of 7800 kg / m3, ρ2 of 1000 kg / m3, ρ3 of 1000 kg / m3 and ρ4 of 2485 kg / m3 respectively; measure the radius of drill collar r1 of 90 mm, the radius of inner well fluid r2 of 27 mm and the radius of outer well fluid r3 of 117 mm; measure the Young's modulus of drill collar and formation as E1 and E2 respectively and the Poisson's ratio as ν1 and ν2 respectively (Young's modulus and Poisson's ratio are inherent parameters of materials);

[0050] S1.3, calculate the borehole diameter r;

[0051] In the forward-looking acoustic logging while drilling, the borehole measurement device is set at an interval of 120°, and the acoustic pulse signal is transmitted in three directions respectively. The array receiver placed on the drill collar captures the echo signal, and then measures the time difference between the time of transmitting the acoustic signal and the time of receiving the reflected pulse signal. According to the acoustic wave velocity, the average borehole diameter r is calculated to be 244.48 mm;

[0052] S2, establish a dispersion model;

[0053] According to the parameters collected in step S1, based on the equal volume gauge invariant condition, the dispersion equation D can be derived using the global matrix method. The specific derivation process is not repeated here. Then, let the dispersion model G equal the determinant of the dispersion equation D, so as to construct the following dispersion model:

[0054]

[0055] in, represents the real wave number, represents the attenuation coefficient and satisfies: is the axial complex wave number of the acoustic wave with frequency ω emitted in the borehole with aperture r, j represents the imaginary part; det[D] represents the determinant of the dispersion equation D;

[0056] In this embodiment, the transfer matrix method may also be used to derive the dispersion equation D. Both the global matrix method and the transfer matrix method are existing methods, and the specific derivation process will not be repeated here.

[0057] S3, dispersion analysis;

[0058] The whole dispersion analysis process is as follows Figure 2 As shown, Figure 2 The depth of the color of the square indicates the value. The white square is 0. The darker the color, the larger the value. s(·) is the sign function.

[0059] S3.1. The dispersion model G is transformed by taking logarithms. The visualization result after transformation is as follows: Figure 3 As shown;

[0060]

[0061] S3.2, Substitute the sound wave signal frequency ω = 1kHz into the logarithmic transformed dispersion model G, and then Sampling is performed separately to obtain Wherein, n=1,2,…,N, m=1,2,…,M, N and M represent the number of samples respectively;

[0062] S3.3, fix first The first point in Will Substitute the values ​​in into the logarithmic transformed dispersion model G to obtain N A matrix of points

[0063]

[0064] S3.4, in the matrix Fill the two ends of the matrix with 0 to get

[0065]

[0066] S3.5. From the matrix The difference operation starts from the second column, that is, each column is subtracted from the previous column elements to obtain the matrix

[0067] S3.6. By introducing symbolic functions The matrix The elements less than 0 are converted to 1, and the elements greater than 0 are converted to 0, resulting in the matrix

[0068] S3.7. From the matrix The difference operation starts from the second column, that is, each column is subtracted from the previous column elements to obtain the matrix Among them, the point corresponding to element -1 is the local minimum of the entire equation;

[0069] S3.8, fix the second point k zrm,2 To the Mth point Repeat steps S3.3 to S3.7 to get the first index matrix

[0070]

[0071] S3.9, Fixed The first point Bundle ) is substituted into the logarithmically transformed dispersion model G, and we get M A matrix of points

[0072] S3.10. According to steps S3.3 to S3.8, obtain the second index matrix

[0073]

[0074] S3.11. Add the two index matrices to obtain the total index matrix

[0075]

[0076] S3.12. Find the total index matrix The point corresponding to the element value of -2 is the local minimum of the dispersion model G in the entire space, that is, the expected wave number to be solved. Finally, all the local minimum points are marked on the dispersion model G, such as Figure 4 As shown;

[0077] S4. Draw the dispersion characteristic curve;

[0078] The frequency ω of the acoustic wave signal emitted by the borehole measurement device is changed to 2kHz, 3kHz, 4kHz, 5kHz to 25kHz in sequence, and step S3 is repeated to obtain the expected wave number corresponding to different frequencies, and then the dispersion characteristic curve is drawn with different frequencies as the horizontal axis and the corresponding expected wave number as the vertical axis.

[0079] Although the above describes the illustrative specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A fast statistical method for dispersion characteristics of acoustic logging while drilling, characterized in that: The following steps are involved: (1) Data collection; (1.1) Setting the frequency ω of the acoustic signal emitted by the borehole measurement device; (1.2) Collect the density of drill collar, inner well fluid, outer well fluid and formation, record them as ρ1, ρ2, ρ3 and ρ4 respectively; measure the radius of drill collar r1, the radius of inner well fluid r2 and the radius of outer well fluid r3; measure the Young's modulus of drill collar and formation as E1 and E2 respectively and Poisson's ratio as ν1 and ν2 respectively; (1.3) Calculate the borehole diameter r; In the forward-looking acoustic logging while drilling, the borehole measurement device is set at an interval of 120°, and the acoustic pulse signal is transmitted in three directions respectively. The array receiver placed on the drill collar captures the echo signal, and then measures the time difference between the time of transmitting the acoustic signal and the time of receiving the reflected pulse signal. According to the acoustic wave velocity, the average borehole diameter r is calculated; (2) Establish a dispersion model; Based on the parameters collected in step (1), the dispersion equation D is derived using the global matrix method, and then the dispersion model G is set equal to the determinant of the dispersion equation D, thereby constructing the following dispersion model: in, represents the real wave number, represents the attenuation coefficient and satisfies: is the complex wave number, j represents the imaginary part; det[D] represents the determinant of the dispersion equation D; (3) Dispersion analysis; (3.1), transform the dispersion model G by taking its logarithm; (3.2), substitute the frequency ω of the acoustic wave signal into the logarithmic transformed dispersion model G, and then Sampling is performed separately to obtain Wherein, n=1,2,…,N, m=1,2,…,M, N and M represent the number of samples respectively; (3.3) First fix The first point in Will Substitute the values ​​in into the logarithmic transformed dispersion model G to obtain N A matrix of points (3.4), in the matrix Fill the two ends of the matrix with 0 to get (3.5), from the matrix The difference operation starts from the second column, that is, each column is subtracted from the previous column elements to obtain the matrix (3.6) By introducing the symbolic function The matrix The elements less than 0 are converted to 1, and the elements greater than 0 are converted to 0, resulting in the matrix (3.7), from the matrix The difference operation starts from the second column, that is, each column is subtracted from the previous column elements to obtain the matrix Among them, the point corresponding to element -1 is the local minimum of the entire equation; (3.8), fix the second point To the Mth point Repeat steps (3.3) to (3.7) to get the first index matrix (3.9), fixed The first point Bundle ) is substituted into the logarithmically transformed dispersion model G, and we get M A matrix of points (3.10) According to steps (3.3) to (3.8), we get the second index matrix (3.11), add the two index matrices together to get the total index matrix (3.12), find the total index matrix The point corresponding to the element value of -2 is the local minimum of the dispersion model G in the entire space, which is the expected wave number to be solved; (4) Draw the dispersion characteristic curve; The frequency ω of the acoustic wave signal emitted by the borehole measurement device is changed to obtain the expected wave number corresponding to different frequencies, and then the dispersion characteristic curve is drawn with different frequencies as the horizontal axis and the corresponding expected wave number as the vertical axis.

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